Properties

Label 112.2.f
Level $112$
Weight $2$
Character orbit 112.f
Rep. character $\chi_{112}(111,\cdot)$
Character field $\Q$
Dimension $4$
Newform subspaces $2$
Sturm bound $32$
Trace bound $3$

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Defining parameters

Level: \( N \) \(=\) \( 112 = 2^{4} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 112.f (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 28 \)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(32\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(112, [\chi])\).

Total New Old
Modular forms 22 4 18
Cusp forms 10 4 6
Eisenstein series 12 0 12

Trace form

\( 4 q + 4 q^{9} + O(q^{10}) \) \( 4 q + 4 q^{9} - 16 q^{21} - 28 q^{25} + 24 q^{29} - 8 q^{37} + 4 q^{49} + 24 q^{53} + 16 q^{57} + 48 q^{65} - 24 q^{77} - 44 q^{81} - 64 q^{93} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(112, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
112.2.f.a 112.f 28.d $2$ $0.894$ \(\Q(\sqrt{-3}) \) None \(0\) \(-4\) \(0\) \(4\) $\mathrm{SU}(2)[C_{2}]$ \(q-2q^{3}-2\zeta_{6}q^{5}+(2-\zeta_{6})q^{7}+q^{9}+\cdots\)
112.2.f.b 112.f 28.d $2$ $0.894$ \(\Q(\sqrt{-3}) \) None \(0\) \(4\) \(0\) \(-4\) $\mathrm{SU}(2)[C_{2}]$ \(q+2q^{3}+2\zeta_{6}q^{5}+(-2-\zeta_{6})q^{7}+q^{9}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(112, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(112, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(28, [\chi])\)\(^{\oplus 3}\)